76 citations · 596 across the 33 of their papers we have counts for
33 papers
Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles
S. E. Derkachov, A. P. Isaev, L. A. Shumilov
We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators for ladder d…
Conformal Triangles and Zig-Zag Diagrams
S. Derkachov, A. P. Isaev, L. Shumilov
A convenient integral representation for zig-zag four-point and two-point planar Feynman diagrams relevant to the bi-scalar D-dimensional fishnet field theory is obtained. This rep…
Elliptic hypergeometric function and -symbols for the SL(2,) group
S. E. Derkachov, G. A. Sarkissian, V. P. Spiridonov
We show that the complex hypergeometric function describing -symbols for group is a special degeneration of the -function -- an elliptic analogue of the E…
Completeness of SoV Representation for Spin Chains
Sergey É. Derkachov, Karol K. Kozlowski, Alexander N. Manashov
This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of…
Separation of variables for the quantum SL(3,C) spin magnet: eigenfunctions of Sklyanin B-operator
S. E. Derkachov, P. A. Valinevich
The quantum SL(3,C) invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of Sklyanin B-operato…
Gustafson Integrals
Sergey E. Derkachov, Alexander N. Manashov, Pavel A. Valinevich
It was shown recently that many of the Gustafson integrals appear in studies of the spin chain models. One can hope to obtain a generalization of the Gusta…